Scientific use of the finite element method in Orthodontics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Complex modal analysis of a vertical rotor through finite element method

Natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical and complex modal analysis. The mathematical modeling was based on the theory of Euler-Bernoulli beam. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using Matlab ®, and numerical simulations were performed to validate this model.

A finite element approach for predicting the ultimate rotation capacity of RC beams

This paper presents a numerical approach to model the complex failure mechanisms that define the ultimate rotational capacity of reinforced concrete beams. The behavior in tension and compression is described by a constitutive damage model derived from a combination of two specific damage models [1]. The nonlinear behavior of the compressed region is treated by the compressive damage model based on the Drucker-Prager criterion written in terms of the effective stresses. The tensile damage model employs a failure criterion based on the strain energy associated with the positive part the effective stress tensor. This model is used to describe the behavior of very thin bands of strain localization, which are embedded in finite elements to represent multiple cracks that occur in the tensioned region [2]. The softening law establishes dissipation energy compatible with the fracture energy of the concrete. The reinforcing steel bars are modeled by truss elements with elastic-perfect plastic behavior. It is shown that the resulting approach is able to predict the different stages of the collapse mechanism of beams with distinct sizes and reinforcement ratios. The tensile damage model and the finite element embedded crack approach are able to describe the stiffness reduction due to concrete cracking in the tensile zone. The truss elements are able to reproduce the effects of steel yielding and, finally, the compressive damage model is able to describe the non-linear behavior of the compressive zone until the complete collapse of the beam due to crushing of concrete. The proposed approach is able to predict well the plastic rotation capacity of tested beams [3], including size-scale effects.

Dynamic analysis for different finite element models of beams with viscoelastic damping layer

Many new viscoelastic materials have been developed recently to help improve noise and vibration levels in mechanical structures for applications in automobile and aeronautical industry. The viscoelastic layer treatment applied to solid metal structures modifies two main properties which are related to the mass distribution and the damping mechanism. The other property controlling the dynamics of a mechanical system is the stiffness that does not change much with the viscoelastic material. The model of such system is usually complex, because the viscoelastic material can exhibit nonlinear behavior, in contrast with the many available tools for linear dynamics. In this work, the dynamic behavior of sandwich beam is modeled by finite element method using different element types which are then compared with experimental results developed in the laboratory for various beams with different viscoelastic layer materials. The finite element model is them updated to help understand the effects in the damping for various natural frequencies and the trade-off between attenuation and the mass add to the structure.

Finite-Element Analysis of Stress on Dental Implant Prosthesis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Influence of Cusp Inclination on Stress Distribution in Implant-Supported Prostheses. A Three-Dimensional Finite Element Analysis

Purpose: The aim of this study was to assess the influence of cusp inclination on stress distribution in implant-supported prostheses by 3D finite element method.Materials and Methods: Three-dimensional models were created to simulate a mandibular bone section with an implant (3.75 mm diameter x 10 mm length) and crown by means of a 3D scanner and 3D CAD software. A screw-retained single crown was simulated using three cusp inclinations (10 degrees, 20 degrees, 30 degrees). The 3D models (model 10d, model 20d, and model 30d) were transferred to the finite element program NeiNastran 9.0 to generate a mesh and perform the stress analysis. An oblique load of 200 N was applied on the internal vestibular face of the metal ceramic crown.Results: The results were visualized by means of von Mises stress maps. Maximum stress concentration was located at the point of application. The implant showed higher stress values in model 30d (160.68 MPa). Cortical bone showed higher stress values in model 10d (28.23 MPa).Conclusion: Stresses on the implant and implant/abutment interface increased with increasing cusp inclination, and stresses on the cortical bone decreased with increasing cusp inclination.

MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

Finite element analysis and fracture resistance testing of a new intraradicular post

Objectives: The objective of the present study was to evaluate a prefabricated intraradicular threaded pure titanium post, designed and developed at the Sao Jose dos Campos School of Dentistry - UNESP, Brazil. This new post was designed to minimize stresses observed with prefabricated post systems and to improve cost-benefits. Materials and and methods: Fracture resistance testing of the post/core/root complex, fracture analysis by microscopy and stress analysis by the finite element method were used for post evaluation. The following four prefabricated metal post systems were analyzed: group 1, experimental post; group 2, modification of the experimental post; group 3, Flexi Post, and group 4, Para Post. For the analysis of fracture resistance, 40 bovine teeth were randomly assigned to the four groups (n=10) and used for the fabrication of test specimens simulating the situation in the mouth. The test specimens were subjected to compressive strength testing until fracture in an EMIC universal testing machine. After fracture of the test specimens, their roots were sectioned and analyzed by microscopy. For the finite element method, specimens of the fracture resistance test were simulated by computer modeling to determine the stress distribution pattern in the post systems studied. Results: The fracture test presented the following averages and standard deviation: G1 (45.63 +/- 8.77), G2 (49.98 +/- 7.08), G3 (43.84 +/- 5.52), G4 (47.61 +/- 7.23). Stress was homogenously distributed along the body of the intraradicular post in group 1, whereas high stress concentrations in certain regions were observed in the other groups. These stress concentrations in the body of the post induced the same stress concentration in root dentin. Conclusions: The experimental post (original and modified versions) presented similar fracture resistance and better results in the stress analysis when compared with the commercial post systems tested (08/2008PA/CEP).

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for Ex (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for Ex modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

Analysis of mechanical behavior in bending of polymer composites using the finite elements method

The use of composite materials has increased in the recent decades, mainly in the aeronautics and automotives industries. In the present study is elaborated a computational simulation program of the bending test using the finite elements method, in the commercial software ANSYS. This simulation has the objective of analyze the mechanical behavior in bending of two composites with polymeric matrix reinforced with carbon fibers. Also are realized bending tests of the 3 points to obtain the resistances of the materials. Data from simulation and tests are used to make a comparison between two failures criteria, Tsai-Wu and Hashin criterion. Copyright © 2009 SAE International.

Comparison of different designs of implant-retained overdentures and fixed full-arch implant-supported prosthesis on stress distribution in edentulous mandible - A computed tomography-based three-dimensional finite element analysis

A finite element analysis was used to compare the effect of different designs of implant-retained overdentures and fixed full-arch implant-supported prosthesis on stress distribution in edentulous mandible. Four models of an human mandible were constructed. In the OR (O'ring) group, the mandible was restored with an overdenture retained by four unsplinted implants with O'ring attachment; in the BC (bar-clip) -C and BC groups, the mandibles were restored with overdentures retained by four splinted implants with bar-clip anchor associated or not with two distally placed cantilevers, respectively; in the FD (fixed denture) group, the mandible was restored with a fixed full-arch four-implant-supported prosthesis. Models were supported by the masticatory muscles and temporomandibular joints. A 100-N oblique load was applied on the left first molar. Von Mises (σvM), maximum (σmax) and minimum (σmin) principal stresses (in MPa) analyses were obtained. BC-C group exhibited the highest stress values (σvM=398.8, σmax=580.5 and σmin=-455.2) while FD group showed the lowest one (σvM=128.9, σmax=185.9 and σmin=-172.1). Within overdenture groups, the use of unsplinted implants reduced the stress level in the implant/prosthetic components (59.4% for σvM, 66.2% for σmax and 57.7% for σmin versus BC-C group) and supporting tissues (maximum stress reduction of 72% and 79.5% for σmax, and 15.7% and 85.7% for σmin on the cortical and trabecular bones, respectively). Cortical bone exhibited greater stress concentration than the trabecular bone for all groups. The use of fixed implant dentures and removable dentures retained by unsplinted implants to rehabilitate edentulous mandible reduced the stresses in the periimplant bone tissue, mucosa and implant/prosthetic components. © 2013 Elsevier Ltd.

Free tools and strategies for the generation of 3D finite element meshes: Modeling of the cardiac structures

The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. © 2013 E. Pavarino et al.

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.